class_docstr: Class for performing sampling in Continuous model
  using Hamiltonian Monte Carlo with dual averaging for
  adaptaion of parameter stepsize.
  
  Parameters:
  -----------
  model: Model from which sampling has to be done
  
  simulate_dynamics: Class to propose future states of position
    and momentum in time by simulating HamiltonianDynamics
  
  delta: float (in between 0 and 1), defaults to 0.65
    The target HMC acceptance probability
  
  References
  -----------
  Matthew D. Hoffman, Andrew Gelman, The No-U-Turn Sampler: Adaptively
  Setting Path Lengths in Hamiltonian Monte Carlo. Journal of
  Machine Learning Research 15 (2014) 1351-1381
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docstr: Run tha adaptation for stepsize for better proposals of position
docstr_tok: ["Run","tha","adaptation","for","stepsize","for","better","proposals","of","position"]
code: def _adapt_params(
      self, stepsize, stepsize_bar, h_bar, mu, index_i, alpha, n_alpha=1
  ):
      """
      Run tha adaptation for stepsize for better proposals of position
      """
      gamma = 0.05  # free parameter that controls the amount of shrinkage towards mu
      t0 = 10.0  # free parameter that stabilizes the initial iterations of the algorithm
      kappa = 0.75
      # See equation (6) section 3.2.1 for details
  
      estimate = 1.0 / (index_i + t0)
      h_bar = (1 - estimate) * h_bar + estimate * (
          self.delta - (alpha / n_alpha)
      )
  
      stepsize = np.exp(mu - ((sqrt(index_i) / gamma) * h_bar))
      i_kappa = index_i ** (-kappa)
      stepsize_bar = np.exp(
          i_kappa * np.log(stepsize)
          + (1 - i_kappa) * np.log(stepsize_bar)
      )
  
      return stepsize, stepsize_bar, h_bar
  
file_path: dragonfly/dragonfly/sampling/hmc.py
imports: from __future__ import division
  from math import sqrt
  import numpy
  from .check_functions import _check_1d_array_object
  from .base import LeapFrog, BaseSimulateHamiltonianDynamics
label_desc: Use image node_id 2 for calling the HamiltonianMCDA obj's underlying member method code with example usage: obj._adapt_params(stepsize, stepsize_bar, h_bar, mu, index_i, alpha, n_alpha) and returns: stepsize,  stepsize_bar,  h_bar